At the opening of three days of arguments, the justices’ questions suggested that they were receptive to a point on which both supporters and opponents of the law agree: that the court should decide the case now rather than waiting until the law’s penalties for not having health insurance become due.

On Tuesday, the court will turn to the central question in the case, the constitutionality of the law’s requirement that most Americans obtain insurance or pay a penalty.

The courtroom on Monday was packed to capacity — some members of the public had waited in line since Friday — and the justices seemed energized, talking over each other more than usual.

Outside, demonstrators came with signs, while Rick Santorum, a candidate for the Republican presidential nomination, made an appearance in front of the courthouse to highlight his opposition to the law — Mr. Obama’s signature legislative accomplishment — and to note that another Republican candidate, Mitt Romney, had signed a state law with similar features when he was the governor of Massachusetts.

The argument on Monday was a sort of appetizer to Tuesday’s main course, a 90-minute debate over whether the court has the authority to hear the case yet, given an 1867 law, the Anti-Injunction Act, that says taxpayers may not challenge taxes until they become due.

The first penalties for violating the health care law’s individual mandate to obtain health insurance do not take effect until 2014, and they must be paid on federal tax returns in April 2015.

“This case presents issues of great moment,” said Solicitor General Donald B. Verrilli Jr., “and the Anti-Injunction Act does not bar the court’s consideration of those issues.”

The justices appeared to agree, and they seemed ready to proceed to the main question. A decision on the constitutionality of the health care law is thus likely by June, as the presidential campaign enters its final stages.

Photo

People lined up at sunrise for tickets to Monday's Supreme Court hearing on President Obama's health care law.Credit
Stephen Crowley/The New York Times

It remains possible, though, that the Anti-Injunction Act will play a role in the case, if at least some of the justices are dissatisfied with the available options during their deliberations and are looking for a way to avoid a decision.

The Anti-Injunction Act says that “no suit for the purpose of restraining the assessment or collection of any tax shall be maintained in any court by any person.” In other words, people who object to taxes must pay first and litigate later.

That is so, said Justice Stephen G. Breyer, because “taxes are, for better or worse, the life’s blood of government.”

The United States Court of Appeals for the Fourth Circuit, in Richmond, Va., ruled last year that the 1867 law left courts for now powerless to decide the health care law’s constitutionality.

The Obama administration had pressed this argument in trial courts but abandoned it on appeal, choosing instead to try to get a quick and clear decision from the courts.

The challengers to the law have always said the law poses no obstacle to immediate review.

In asking the Supreme Court to hear the case last year, the administration suggested that the justices appoint an outside lawyer to argue that the law bars the challenges. The justices asked Robert A. Long, a Washington lawyer in private practice, to do so, and he went first on Monday.

“I would not argue that this statute is a perfect model of clarity,” Mr. Long said. But he said law was “jurisdictional,” meaning it forbids courts from hearing suits even if, as here, neither side objected.

Mr. Long was followed by Mr. Verrilli, the solicitor general, arguing for the Obama administration, and Gregory G. Katsas, who represents the private parties challenging the law.

Mr. Verrilli, whose style of argument is sober and deliberate, will return on Tuesday, arguing against two more colorful lawyers: Paul D. Clement, representing the 26 states challenging the law, and Michael A. Carvin, representing the private challengers.

Video

TimesCast | March 26, 2012

The Supreme Court opens hearings on the 2010 health care law, and a look at the partisan division behind the bill's individual mandate.

Mr. Verrilli walked a fine line on Monday. He told the court that the administration wanted a prompt ruling on the health care law and that the 1867 law should not stand in the way. At the same time, he asked the justices not to damage the federal government’s ability to rely on the 1867 law in other cases.

There were other complications. Mr. Verrilli’s argument that the penalty is not a tax for purposes of the 1867 law was in potential tension with one he will make on Tuesday, that the mandate was authorized not only by Congress’s power under the commerce clause but also by its power to levy taxes.

“Today you are arguing that the penalty is not a tax,” Justice Samuel A. Alito Jr. said. “Tomorrow you are going to be back, and you will be arguing that the penalty is a tax.”

Mr. Verrilli said the name Congress gave to the payment required for violating the mandate in the health care law — calling it a penalty, not a tax — mattered for purposes of the 1867 law but was irrelevant in connection with the constitutional taxing power.

The challengers to the law, represented by Mr. Katsas, agreed with Mr. Verrilli that the court might decide the case on the merits now. Mr. Katsas said the penalty for failing to obtain insurance was not the sort of tax the 1867 law concerned.

Mr. Katsas also said that the challenge was in any event to the mandate, which applies to virtually every American, rather than to the penalty, which applies to a smaller group.

Among people subject to the mandate but not the penalty, according to the challengers, are some poor people, members of some Indian tribes and those uninsured during gaps in coverage.

“The purpose of this lawsuit is to challenge a federal requirement to buy health insurance,” Mr. Katsas said. “That requirement itself is not a tax. And for that reason alone, we think the Anti-Injunction Act doesn’t apply.”

In a brief, the states challenging the health care law pressed a further argument. They say that the 1867 law does not apply to them, because states do not pay taxes, even if it applies to the private challengers.

At the conclusion of Monday’s argument, Chief Justice John G. Roberts Jr. thanked Mr. Long for his assistance to the court and added, superfluously, that “we will continue argument in this case tomorrow.”

A version of this article appears in print on March 27, 2012, on page A16 of the New York edition with the headline: Three Days of Hearings on Health Law Begin Before the Supreme Court. Order Reprints|Today's Paper|Subscribe